## Abstract

We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level ℓ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce S-evaluation on the set of dominant maximal weights for each highest modules, and generalize Sagan's action in [17] by considering the datum on each affine Kac-Moody algebra. As consequences, we obtain closed and recursive formulae for cardinality of the number of dominant maximal weights for every highest weight module and observe level-rank duality on the cardinalities.

Original language | English |
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Article number | 107336 |

Journal | Advances in Mathematics |

Volume | 374 |

DOIs | |

State | Published - 18 Nov 2020 |

## Keywords

- Affine Kac-Moody algebra
- Cyclic sieving phenomenon
- Dominant maximal weight